This code is an example of how you could use Python to optimize the design of an energy system. The energy system is defined by two variables: the energy input (in MW) and the efficiency of the system (dimensionless). The goal is to find the optimal value of the energy input that will result in the lowest cost for the system.

To do this, the code defines a function called `cost`

that calculates the cost of the energy system as a function of the energy input and the efficiency. This function takes into account the cost of the energy input itself, as well as the efficiency of the system (since a more efficient system will have a lower cost).

Then, the code uses an optimization algorithm to find the optimal value of the energy input that minimizes the `cost`

function. The optimization algorithm is given the starting value of the energy input, and it iteratively adjusts this value to find the minimum of the `cost`

function.

Finally, the code generates a grid of possible energy input values and calculates the cost at each point on the grid. It then plots the cost as a function of the energy input, with the starting energy input indicated by a red dot and the optimal energy input indicated by a blue dot. The resulting plot can be used to visualize how the cost of the energy system changes as a function of the energy input, and to see how the optimal energy input compares to the starting energy input.

```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Dec 21 22:53:22 2022
@author: ramnot
"""
import numpy as np
import scipy.optimize as optimize
import matplotlib.pyplot as plt
# Define variables for the energy system
energy_input = 10 # MW
energy_output = 8 # MW
efficiency = energy_output / energy_input # dimensionless
# Define the cost function
def cost(energy_input, efficiency):
# Assume a cost of $1000/MW for energy input
return energy_input * 1000 + efficiency**2
# Use optimization algorithm to find the optimal energy input
result = optimize.minimize(cost, energy_input, args=(efficiency,), method='nelder-mead')
optimal_energy_input = result.x
# Generate a grid of energy input values
energy_input_range = np.linspace(0, 20, 100)
# Calculate the cost at each point on the grid
cost_values = np.zeros_like(energy_input_range)
for i in range(energy_input_range.shape[0]):
cost_values[i] = cost(energy_input_range[i], efficiency)
# Plot the cost as a function of the energy input
fig, ax = plt.subplots(figsize=(8,6))
ax.plot(energy_input_range, cost_values)
ax.plot(energy_input, cost(energy_input, efficiency), 'o', color='red', label='Starting energy input')
ax.plot(optimal_energy_input, cost(optimal_energy_input, efficiency), 'o', color='blue', label='Optimal energy input')
ax.set_xlabel('Energy input (MW)', fontsize=12)
ax.set_ylabel('Cost (USD)', fontsize=12)
ax.legend(fontsize=12)
plt.show()
```